BL-final.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1027,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import interpolate\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Polygon \n",
    "from pylab import figure, show, legend, ylabel\n",
    "from math import e, pi, isinf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1545,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class BuckleyLev():\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.params = {\n",
    "            #non wetting phase viscosity\n",
    "            \"viscosity_o\": 1.e-3,\n",
    "            #wetting phase viscosity\n",
    "            \"viscosity_w\": 0.5e-3,\n",
    "            #initial water sat\n",
    "            \"initial_sw\":0.4,\n",
    "            #residual water saturation, Swirr\n",
    "            \"residual_w\":0.1,\n",
    "            #residual oil saturation, Sor\n",
    "            \"residual_o\":0.1,\n",
    "            #connate water saturation \n",
    "            #water rel perm at water curve end point\n",
    "            \"krwe\":1,\n",
    "            #oil rel perm at oil curve end point\n",
    "            \"kroe\": 0.9,\n",
    "            #dimless velocity results\n",
    "            'vd_array':[],\n",
    "            #porosity\n",
    "            'poro':0.24,\n",
    "            #water injection rate units m3/hr\n",
    "            \"inject_rate\":200,\n",
    "            #cross sectional area units m2\n",
    "            \"x-area\":30\n",
    "        }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1546,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def k_rw(self,sw):\n",
    "    #water relative perm calculation for a given water saturation \n",
    "    p = 11.174\n",
    "    return ((self.params['krwe']))*sw**p\n",
    "\n",
    "BuckleyLev.k_rw = k_rw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1547,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def k_rn(self,sw):\n",
    "    #oil relative perm calculation for a given water saturation \n",
    "    q = 3.326\n",
    "    return ((1.-self.params['kroe']*sw)**q)\n",
    "\n",
    "BuckleyLev.k_rn = k_rn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1548,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fractional_flow(self,sw):\n",
    "    #returns the fractional flow\n",
    "    \n",
    "    return 1./(1.+((self.k_rn(sw)/self.k_rw(sw))*(self.params[\"viscosity_w\"]/self.params[\"viscosity_o\"])))\n",
    "\n",
    "BuckleyLev.fractional_flow = fractional_flow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1549,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_fractional_flow(self):\n",
    "    #plot the sw vs fractional flow\n",
    "    \n",
    "    #x = np.linspace(self.params[\"residual_w\"]+1e-3,(1-self.params[\"residual_o\"]+1e-3),100)\n",
    "    x = np.linspace(self.params[\"residual_w\"]+1e-3,(1-self.params[\"residual_o\"]),100)\n",
    "    y = [self.fractional_flow(i) for i in x ]\n",
    "    \n",
    "    plt.plot(x,y)\n",
    "    \n",
    "    #sw_at_front = self.sw_at_shock_front()\n",
    "    #plt.plot([sw_at_front],[self.fractional_flow(sw_at_front)],'ro')\n",
    "    \n",
    "    plt.title('Fractional flow as a function of water saturation')\n",
    "    plt.xlabel('Sw')\n",
    "    plt.ylabel('Fractional flow')\n",
    "    plt.ylim([0,1.1])\n",
    "    plt.xlim([0,1])\n",
    "    \n",
    "    #add limiting fractional flow lines\n",
    "    plt.hlines(y[len(y)-1],0,1,linestyles='dashed',lw=2, colors='0.4')\n",
    "    plt.annotate('fw max: %.4f' % y[len(y)-1],xy=(0.08,0.95))\n",
    "    \n",
    "    \n",
    "    #plt.show()\n",
    "    #print(y[len(y)-1])\n",
    "    \n",
    "BuckleyLev.plot_fractional_flow = plot_fractional_flow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1550,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fractional_flow_deriv(self,sw):\n",
    "    #calculate derivative of fractional flow - dFw/dSw - Vsh\n",
    "    \n",
    "    f_deriv = (self.fractional_flow(sw+0.0001) - self.fractional_flow(sw))/0.0001\n",
    "    \n",
    "    return f_deriv\n",
    "\n",
    "BuckleyLev.fractional_flow_deriv = fractional_flow_deriv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1551,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_fractional_flow_deriv(self):\n",
    "    #plot the derivative dFw/dSw - Vsh vs Sw\n",
    "    x = np.linspace(self.params[\"residual_w\"]+1e-3,(1-self.params[\"residual_o\"]),100)\n",
    "    y = [self.fractional_flow_deriv(i) for i in x ]\n",
    "    \n",
    "    plt.plot(x,y)\n",
    "    plt.title('Derivative of fractional flow curve')\n",
    "    plt.ylabel('dfw/dSw')\n",
    "    plt.xlabel('Sw')\n",
    "    plt.show()\n",
    "    \n",
    "BuckleyLev.plot_fractional_flow_deriv=plot_fractional_flow_deriv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1552,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def frac_deriv_combo(self):\n",
    "    x = np.linspace(self.params[\"residual_w\"]+1e-3,((1-self.params[\"residual_o\"])),100)\n",
    "    # is the fractional flow curve\n",
    "    y = [self.fractional_flow(i) for i in x ]\n",
    "    \n",
    "    #y2 is the derivative\n",
    "    y2 = [self.fractional_flow_deriv(i) for i in x ]\n",
    " \n",
    "    fig1 = figure()\n",
    "    \n",
    "    ax1 = fig1.add_subplot(111)\n",
    "    line1 = ax1.plot(x,y,lw=2)\n",
    "    ylabel(\"Fractional flow\")\n",
    "    ax1.set_ylim([0,1.2])\n",
    "  \n",
    "    \n",
    "    ax2 = fig1.add_subplot(111, sharex=ax1, frameon=False)\n",
    "    line2 = ax2.plot(x,y2,'-r',lw=2)\n",
    "    ax2.yaxis.tick_right()\n",
    "    ax2.yaxis.set_label_position(\"right\")\n",
    "    ylabel(\"Derivative dfw/dsw\")\n",
    "    ax2.set_xlim([0.4,1])\n",
    "    \n",
    "    plt.title('Fractional flow as a function of water saturation')\n",
    "    \n",
    "    plt.xlabel('Sw')\n",
    "    \n",
    "    ax1.hlines(y[len(y)-1],0,1,linestyles='dashed',lw=2, colors='0.4')\n",
    "    ax1.annotate('fw max: %.4f' % y[len(y)-1],xy=(0.85,1.02))\n",
    "    \n",
    "    \n",
    "    ax1.spines['left'].set_color('blue')\n",
    "    ax1.tick_params(axis='y', colors='blue')\n",
    "    \n",
    "    ax1.spines['right'].set_color('red')\n",
    "    ax2.tick_params(axis='y', colors='red')\n",
    "    \n",
    "\n",
    "    show()\n",
    "    \n",
    "BuckleyLev.frac_deriv_combo = frac_deriv_combo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1553,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#generate xt curve for a given time step, if no time step, timwe =1 \n",
    "def xt(self,time=1):\n",
    "    \n",
    "    flux = ((self.params['inject_rate'])/(60.0*60.0))/self.params['x-area']\n",
    "    td = (flux*time)/(self.params['x-area']*self.params['poro'])\n",
    "    \n",
    "    y = np.linspace(self.params[\"residual_w\"]+1e-3,(1-self.params[\"residual_o\"]),50)\n",
    "    x = [(self.fractional_flow_deriv(i))*td for i in y]\n",
    "    \n",
    "    return(x,y)\n",
    "\n",
    "BuckleyLev.xt = xt\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1554,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def shock_sat(self):\n",
    "    \n",
    "    #create dx window of increasing size for calculating welge\n",
    "\n",
    "    x = np.linspace(self.params[\"residual_w\"]+1e-3,(1-self.params[\"residual_o\"]),100)\n",
    "    y = [self.fractional_flow(i) for i in x ]\n",
    "  \n",
    "    maximum, sw_shock = 0,0\n",
    "    grads = []\n",
    "    \n",
    "    for index,item in enumerate(y):\n",
    "        \n",
    "        grad = (item - (y[0]+0.00001))/(x[index]-(x[0]+0.001)) \n",
    "        \n",
    "        \n",
    "        if grad>maximum:\n",
    "            #plt.plot([self.params[\"residual_w\"]+1e-3,x[index]],[0,item],'o-')\n",
    "            sw_shock = x[index]\n",
    "            maximum = grad\n",
    "    \n",
    "    #plt.show()\n",
    "    #print(sw_shock)\n",
    "    return(sw_shock)\n",
    " \n",
    "\n",
    "BuckleyLev.shock_sat = shock_sat\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1555,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = BuckleyLev()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1556,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "shk = a.shock_sat()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1557,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a.plot_fractional_flow()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1558,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1107a9dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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t3ueKFXDLLeYySxZ96sSYonOXHQJ0BG4Fyqhq7TDtYmrJiJAC9A0EOxToKkLj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10efb4c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "a.frac_deriv_combo()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1559,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_xd(self,times=[1]):\n",
    "    \n",
    "    colors = {0:'r',1:'b',2:'c',3:'g'}\n",
    "    max_val = 0\n",
    "    \n",
    "    for index,time in enumerate(times):\n",
    "        if (max(a.xt(time)[0]) > max_val):\n",
    "            max_val = max(a.xt(time)[0])\n",
    "            \n",
    "        plt.plot(a.xt(time)[0],a.xt(time)[1],colors[index],lw=2)\n",
    "\n",
    "    plt.hlines(self.shock_sat(),0,7,linestyles='dashed',lw=2, colors='0.4')\n",
    "    \n",
    "    plt.annotate('Sw shock: %.2f' % self.shock_sat(),xy=(max_val-1.3,self.shock_sat()+0.012))\n",
    "    plt.ylim([0,1])\n",
    "    plt.show()\n",
    "    \n",
    "BuckleyLev.plot_xd = plot_xd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1560,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def slice_rarefaction(self,time):\n",
    "    \n",
    "    #generate the xt data \n",
    "    xt, sw = self.xt(time)\n",
    "    index = 0\n",
    "\n",
    "    #find out where the shock saturation is\n",
    "    shock_sat = self.shock_sat()\n",
    "    \n",
    "    #now trim xt and sw arrays \n",
    "    for index, item in enumerate(sw):\n",
    "        if item >= shock_sat:\n",
    "            lim = index\n",
    "            break\n",
    "            \n",
    "    sw_trim = (sw[lim:])\n",
    "    xt_trim = (xt[lim:])\n",
    "  \n",
    "    return(sw_trim,xt_trim)\n",
    "    \n",
    "    \n",
    "    \n",
    "BuckleyLev.slice_rarefaction = slice_rarefaction\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1561,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bNnNf+X//t2O64eRkuO46uP12r0ytMyi0Wix8XVPD6spKPq6oIKe21qmeOiww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\nQJd9iOilAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eeb3e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = BuckleyLev()\n",
    "a.plot_xd([1000,2000,3000,4000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1562,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.83477551,  0.85108163,  0.86738776,  0.88369388,  0.9       ]),\n",
       " [0.2233635765433416,\n",
       "  0.15356318003323696,\n",
       "  0.10420268985441156,\n",
       "  0.069858357148850872,\n",
       "  0.046269935048767051])"
      ]
     },
     "execution_count": 1562,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.slice_rarefaction(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1563,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_sat_front(self,times=[1]):\n",
    "    colors = {0:'r',1:'b',2:'c',3:'g'}\n",
    "       \n",
    "    for index, time in enumerate(times):\n",
    "        \n",
    "        y = sorted((self.slice_rarefaction(time)[0]))\n",
    "        x = sorted((self.slice_rarefaction(time)[1]),reverse=True)\n",
    "        plt.plot(x,y,colors[index],lw=2)\n",
    "\n",
    "        if (x[len(x)-1]>0.001):\n",
    "            #plt.plot([0,x[len(x)-1]],[1,1],'b',lw=2)\n",
    "            plt.hlines(1-self.params[\"residual_o\"],0,x[len(x)-1],colors[index],lw=2)\n",
    "            plt.plot(x[len(x)-1],y[len(y)-1],colors[index]+'o')\n",
    "\n",
    "\n",
    "        plt.vlines(x[0],y[0],self.params[\"initial_sw\"],colors[index],lw=2)\n",
    "        plt.hlines(self.params[\"initial_sw\"],x[0],x[0]+1,colors[index],lw=2)\n",
    "\n",
    "        #highlight vshock point\n",
    "        plt.plot(x[0],y[0],colors[index]+'o') \n",
    "\n",
    "    plt.ylim([0,1])\n",
    "    plt.xlim([0,x[0]+1])\n",
    "    \n",
    "    plt.show()\n",
    "BuckleyLev.plot_sat_front = plot_sat_front"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1565,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kZcwQl6SMGeKSlDFDXJIyZohLUsYMcUnKmCEuSRkzxCUpY4a4JGXMEJekjBnikpQxQ1yS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\nXJIyZohLUsb+PzTe/qhgk7SXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f4d2ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = BuckleyLev()\n",
    "a.plot_sat_front([500,2000,3000,4000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1486,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ro'"
      ]
     },
     "execution_count": 1486,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "colors = {1:'r',2:'b'}\n",
    "colors[1]+'o'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}